PURE MTH 7106  Algebra
North Terrace Campus  Semester 1  2020

General Course Information
Course Details
Course Code PURE MTH 7106 Course Algebra Coordinating Unit School of Mathematical Sciences Term Semester 1 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 4 hours per week Available for Study Abroad and Exchange Y Assumed Knowledge MATHS 1012 Course Description Knowledge of group theory and of linear algebra is important for an understanding of many areas of pure and applied mathematics, including advanced algebra and analysis, number theory, coding theory, cryptography and differential equations. There are also important applications to physics and chemistry.
Topics covered are (1) Equivalence relations (2) Groups: subgroups, cyclic groups, cosets, Lagrange's theorem, normal subgroups and factor groups. Examples of finite and infinite groups, including groups of symmetries and permutations, groups of numbers and matrices. Homomorphisms and isomorphisms of groups. (3) Linear algebra: vector spaces, bases, linear transformations and matrices, subspaces, sums and quotients of spaces, dual spaces, bilinear forms and inner product spaces, and canonical forms.Course Staff
Course Coordinator: Associate Professor Nicholas Buchdahl
Course Timetable
The full timetable of all activities for this course can be accessed from Course Planner.

Learning Outcomes
Course Learning Outcomes
 Appreciate that common features of certain mathematical objects can be abstracted and studied.
 Understand equivalence relations and partitions.
 Understand the concepts of groups, group homomorphism and isomorphism and related notions.
 Be familiar with common examples of groups of both finite and infinite order.
 Be able to construct and work with related objects: subgroups, cartesian products, quotient groups.
 Understand what it means for a group to act on a set.
 Understand the concepts of vector space, linear transformation, isomorphism and related notions.
 Be able to construct and work with related objects: subspaces, sums, quotient spaces, dual spaces.
 Understand the notion of bilinear form.
 Understand the significance of Jordan canonical form.
 Be familiar with various methods of proof, including direct proof, constructive proof, proof by contradiction, induction.
 Develop skills in creative and critical thinking, problem solving, logical writing and clear communication of mathematical ideas.
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Deep discipline knowledge
 informed and infused by cutting edge research, scaffolded throughout their program of studies
 acquired from personal interaction with research active educators, from year 1
 accredited or validated against national or international standards (for relevant programs)
all Critical thinking and problem solving
 steeped in research methods and rigor
 based on empirical evidence and the scientific approach to knowledge development
 demonstrated through appropriate and relevant assessment
all Teamwork and communication skills
 developed from, with, and via the SGDE
 honed through assessment and practice throughout the program of studies
 encouraged and valued in all aspects of learning
12 Career and leadership readiness
 technology savvy
 professional and, where relevant, fully accredited
 forward thinking and well informed
 tested and validated by work based experiences
12 
Learning Resources
Required Resources
None.Recommended Resources
 Fraleigh, J. B.: A first course in abstract algebra (Addison Wesley).
 Durbin, J. R.: Modern algebra (Wiley).
 Herstein, I. N.: Topics in Algebra (Wiley).
 Lay, D. C.: Linear algebra and its applications (Pearson).
 Lipschutz, S.: Linear algebra (Schaum's Outline Series).
 Katznelson, Y. & Katznelson, Y. R.: A (terse) introduction to linear algebra (AMS).
 Axler, S.: Linear Algebra Done Right (Springer).
Online Learning
This course uses Canvas for providing electronic resources, such as lecture notes, assignment papers, sample solutions, etc. It is recommended that students make appropriate use of these resourses.

Learning & Teaching Activities
Learning & Teaching Modes
This course relies on lectures as the primary delivery mechanism for the material. Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through the lectures. Written assignments aid the learning of the material and provide assessment opportunities for students to gauge their progress and understanding.Workload
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload Hours Lectures 36 90 Tutorials 6 21 Assignments 5 45 Total 156 Learning Activities Summary
Lecture Outline Binary operations, groups, subgroups (2 lectures).
 Permutations, symmetric and alternating groups (2 lectures).
 Isomorphism of groups (1 lecture).
 Equivalence relations (1 lecture).
 Cosets and Lagrange's Theorem (2 lectures).
 Group homomorphisms (2 lectures).
 Normal subgroups and factor groups, simple groups, First Isomorphism Theorem (2 lectures).
 Groups acting on sets. Cauchy's theorem. (3 lectures).
 Symmetry and the dihedral groups. (2 lectures)
 Vector spaces, subspaces, linear independence, basis, dimension (3 lectures).
 Linear transformations. Sums and quotients of vector spaces. (3 lectures).
 Matrix with respect to basis, eigenvectors, similarity, dimension theorem (2 lectures).
 Linear functionals and the dual space, second dual space (1 lecture).
 Bilinear forms, congruent matrices, symmetric bilinear forms, quadratic forms (2 lectures).
 Inner products, norm, distance, orthogonality (2 lectures).
 Adjoints (1 lectures).
 Jordan canonical form (3 lectures).
 Tutorial 1: Groups.
 Tutorial 2: Permutations, isomorphism.
 Tutorial 3: Normal subgroups, quotient groups.
 Tutorial 4: Sums of spaces.
 Tutorial 5: Matrix of a linear transformation, linear functionals.
 Tutorial 6: Bilinear forms. Jordan canonical form.
The lecture contents will be adjusted based on students' actual learning progress and outcome.Specific Course Requirements
None.Small Group Discovery Experience
None. 
Assessment
The University's policy on Assessment for Coursework Programs is based on the following four principles:
 Assessment must encourage and reinforce learning.
 Assessment must enable robust and fair judgements about student performance.
 Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
 Assessment must maintain academic standards.
Assessment Summary
Due to the current COVID19 situation modified arrangements have been made to assessments to facilitate remote learning and teaching. Assessment details provided here reflect recent updates.
Component Weighting Objective Assessed Fortnightly Assignments# 25% all Weekly quizzes^ 25% all Midterm test 20% 15, 12 Final Exam 30% all
#Fortnightly homework assignments are distributed on MyUni as they have been on Wednesdays of even weeks and due on Fridays at 3pm of the following week;
^The first such quiz will be available this coming weekend (2829 March), but it will not count at all: it will be used as an experiment to see how well the system works. But it should be of about the same length and level of difficulty that you can expect in general. Feedback will be very helpful.Assessment Related Requirements
An aggregate score of at least 50% is required to pass the course.Assessment Detail
No information currently available.
Submission
Assignments will have a 2week turnaround time for feedback to students.Course Grading
Grades for your performance in this course will be awarded in accordance with the following scheme:
M10 (Coursework Mark Scheme) Grade Mark Description FNS Fail No Submission F 149 Fail P 5064 Pass C 6574 Credit D 7584 Distinction HD 85100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through Access Adelaide.

Student Feedback
The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including ongoing engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.
SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

Student Support
 Academic Support with Maths
 Academic Support with writing and speaking skills
 Student Life Counselling Support  Personal counselling for issues affecting study
 International Student Support
 AUU Student Care  Advocacy, confidential counselling, welfare support and advice
 Students with a Disability  Alternative academic arrangements
 Reasonable Adjustments to Teaching & Assessment for Students with a Disability Policy
 LinkedIn Learning

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 Assessment for Coursework Programs
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 Modified Arrangements for Coursework Assessment
 Student Experience of Learning and Teaching Policy
 Student Grievance Resolution Process

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